J.M. Lattimer and M. Prakash. The Physics of Neutron Stars.pdf

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The Physics of Neutron Stars

If true, such matter is the ultimate ground state of matter. Normal matter is
then metastable, and compressed to sufficiently high density, would spontaneously convert to deconfined quark matter. Unlike normal stars, SQM stars
are self-bound, not requiring gravity to hold them together. It is generally assumed that pulsars and other observed neutron stars are normal neutron
stars. If SQM stars have a bare quark surface, calculations suggest that photon
emission from SQM stars occurs primarily in the energy range 30 keV < E <
500 keV [11].

How Neutron Stars are Formed
Neutron stars are created in the aftermath of the gravitational collapse of the
core of a massive star (> 8 M ) at the end of its life, which triggers a Type II
supernova explosion. Newly born neutron stars or proto-neutron stars are rich
in leptons, mostly e − and ße (Fig. 1). The detailed explosion mechanism of Type
II supernovae is not understood [12], but it is probable that neutrinos play a
crucial role. One of the most remarkable aspects is that neutrinos become temporarily trapped within the star during collapse. The typical neutrino-matter
cross section is ã ≈ 10−40 cm2 , resulting in a mean free path Ý ≈ (ãn)−1 ≈ 10
cm, where the baryon number density is n ' 2 to 3 n0 . This length is much
less than the proto-neutron star radius, which exceeds 20 km. The gravitational binding energy released in the collapse of the progenitor star’s white
dwarf-like core to a neutron star is about 3G M/5R 2 ' 3 × 1053 erg (G is the
gravitational constant), which is about 10% of its total mass energy Mc 2 . The
kinetic energy of the expanding remnant is in the order of 1×1051 to 2×1051
erg, and the total energy radiated in photons is further reduced by a factor
of 100. Nearly all the energy is carried off by neutrinos and antineutrinos of
all flavors in roughly equal proportions. Core collapse halts when the star’s
interior density reaches n0 , which triggers the formation of a shock wave at
the core’s outer edge. The shock wave propagates only about 100 to 200 km
before it stalls, having lost energy to neutrinos and from nuclear dissociation
of the material it has plowed through [stage (I) in Fig. 1]. Apparently, neutrinos
from the core, assisted perhaps by rotation, convection and magnetic fields,
eventually resuscitate the shock, which within seconds accelerates outwards,
expelling the massive stellar mantle. The proto-neutron star left behind rapidly
shrinks because of pressure losses from neutrino emission in its periphery
(stage II). The escape of neutrinos from the interior occurs on a diffusion time
ä ' 3R 2 /Ýc ≈ 10 s. The neutrinos observed from Supernova (SN) 1987A in
the Large Magellanic Cloud confirmed this time scale and the overall energy
release of ' 3 × 1053 ergs [13, 14, 15, 16].
The loss of neutrinos (which forces electrons and protons to combine, making
the matter more neutron-rich) initially warms the stellar interior. The core temperature more than doubles (stage III), reaching ∼ 50 MeV (6 × 1011 K). After 10
to 20 s, however, the steady emission of neutrinos begins to cool the interior.
Because the cross section ã ∝ Ý−1 scales as the square of the mean neutrino
energy, the condition Ý > R is achieved in about 50 s. The star becomes transparent to neutrinos (stage IV), and its cooling rate accelerates.
Neutron stars have both minimum and maximum mass limits. The maximum